LDA final project
Kaitlin Maciejewski, Morgan de Ferrante, Bingnan Li, Volha Tryputsen
Exploratory
Smoking vs. Age, Sex
(1): Smoking ~ age, sex
Is there a relationship between age and smoking status?
ANS: Yes, the proportion of smokers decreases with the age.
data %>%
select(cursmoke, age) %>%
ggplot(aes(x = age, y = cursmoke)) +
geom_jitter(height = 0.1, alpha = 0.1) +
geom_smooth(lwd = 1.5) +
theme_bw() 
Does this relationship differ by sex?
ANS: There is a higher proportion of smoker among men compared to women as both age ,but there is no interaction between age and sex.
data %>%
select(cursmoke, age, sex) %>%
ggplot(aes(x = age, y = cursmoke, group = sex, color = sex)) +
geom_jitter(height = 0.1, alpha = 0.1) +
geom_smooth(lwd = 1.5) +
theme_bw() 
(2) number of cigarettes ~ age, sex
Is there a relationship between the number of cigarettes smoked per day and age?
ANS: Yes, number of sigarets smoked per day stays constant for 30-50 years old and decreases with age after 50 years old.
All
data %>%
select(cigpday, age) %>%
ggplot(aes(x = age, y = cigpday)) +
geom_jitter(height = 0.1, alpha = 0.1) +
geom_smooth(lwd = 1.5) +
theme_bw() ## Warning: Removed 79 rows containing non-finite values (stat_smooth).## Warning: Removed 79 rows containing missing values (geom_point).
Smokers only
data %>%
select(cigpday, age) %>%
filter(cigpday > 0) %>%
ggplot(aes(x = age, y = cigpday)) +
geom_jitter(height = 0.1, alpha = 0.1) +
geom_smooth(lwd = 1.5) +
theme_bw() 
Does this relationship differ by sex?
ANS: There is sex effect (men smoke higer number of sigarets per day than women across age), but there is no sex and age interaction.
All
data %>%
select(cigpday, age, sex) %>%
ggplot(aes(x = age, y = cigpday, group = sex, color = sex)) +
geom_jitter(height = 0.1, alpha = 0.1) +
geom_smooth(lwd = 1.5) +
theme_bw() ## Warning: Removed 79 rows containing non-finite values (stat_smooth).## Warning: Removed 79 rows containing missing values (geom_point).
Smokers only
data %>%
select(cigpday, age, sex) %>%
filter(cigpday > 0) %>%
ggplot(aes(x = age, y = cigpday, group = sex, color = sex)) +
geom_jitter(height = 0.1, alpha = 0.1) +
geom_smooth(lwd = 1.5) +
theme_bw() 
Smoking vs. health outcomes
(1) The relationship between current smoking status and systolic blood pressure.
smoking ~ sysbp
ANS: Proportion of smokers decreases with increase of systolic blood presure
data %>%
select(cursmoke, sysbp) %>%
ggplot(aes(x = sysbp, y = cursmoke)) +
geom_jitter(height = 0.1, alpha = 0.1) +
geom_smooth(lwd = 1.5) +
theme_bw() 
ANS: slightly higher sysbp for non-smokers
data %>%
select(cursmoke, sysbp) %>%
mutate(cursmoke = factor(cursmoke)) %>%
ggplot(aes(y = sysbp, x = cursmoke)) +
geom_boxplot(outlier.colour = "white") +
theme_bw() 
smoking ~ sysbp, sex
ANS: Proportion of smokers decreases with increase of systolic blood presure; the proportion is higher for men (sex effect).
data %>%
select(cursmoke, sysbp, sex) %>%
ggplot(aes(x = sysbp, y = cursmoke, group = sex, color = sex)) +
geom_jitter(height = 0.1, alpha = 0.1) +
geom_smooth(lwd = 1.5) +
theme_bw() 
ANS: no differences in sysbp between male and female smokers and non-smokers
data %>%
select(cursmoke, sex, sysbp) %>%
mutate(cursmoke = factor(cursmoke),
smoke_sex = interaction(cursmoke, sex)) %>%
ggplot(aes(y = sysbp, x = smoke_sex)) +
geom_boxplot(outlier.colour = "white") +
theme_bw() 
(2) The relationship between current smoking status and diastolic blood pressure.
smoking ~ diabp
ANS: Proportion of smokers decreases with increase of diastolic blood presure for BP=100 ad then proportion increases again (latter could be due to not enough data)
data %>%
select(cursmoke, diabp) %>%
ggplot(aes(x = diabp, y = cursmoke)) +
geom_jitter(height = 0.1, alpha = 0.1) +
geom_smooth(lwd = 1.5) +
theme_bw() 
ANS: no difference
data %>%
select(cursmoke, diabp) %>%
mutate(cursmoke = factor(cursmoke)) %>%
ggplot(aes(y = diabp, x = cursmoke)) +
geom_boxplot(outlier.colour = "white") +
theme_bw() 
smoking ~ diabp, sex
ANS: Proportion of smokers decreases with increase of diastolic blood presure; the proprtions are higher for men (sex effect).
data %>%
select(cursmoke, diabp, sex) %>%
ggplot(aes(x = diabp, y = cursmoke, group = sex, color = sex)) +
geom_jitter(height = 0.1, alpha = 0.1) +
geom_smooth(lwd = 1.5) +
theme_bw() 
ANS: no difference
data %>%
select(cursmoke, sex, diabp) %>%
mutate(cursmoke = factor(cursmoke),
smoke_sex = interaction(cursmoke, sex)) %>%
ggplot(aes(y = diabp, x = smoke_sex)) +
geom_boxplot(outlier.colour = "white") +
theme_bw() 
(3) The relationship between current smoking status and serum total cholesterol.
smoking ~ totchol
ANS: Proportion of smokers slightly decreases with increase of total cholesterol values
data %>%
select(cursmoke, totchol) %>%
ggplot(aes(x = totchol, y = cursmoke)) +
geom_jitter(height = 0.1, alpha = 0.1) +
geom_smooth(lwd = 1.5) +
theme_bw() ## Warning: Removed 409 rows containing non-finite values (stat_smooth).## Warning: Removed 409 rows containing missing values (geom_point).
ANS: no difference
data %>%
select(cursmoke, totchol) %>%
mutate(cursmoke = factor(cursmoke)) %>%
ggplot(aes(y = totchol, x = cursmoke)) +
geom_boxplot(outlier.colour = "white") +
theme_bw() ## Warning: Removed 409 rows containing non-finite values (stat_boxplot).
smoking ~ totchol, sex [!!!]
ANS: Proportion of smokers hasnonlinera relationship with total cholesterol for women; proprtions increases with increase in total cholesterol for men (sex by totchol interaction effect).
data %>%
select(cursmoke, totchol, sex) %>%
ggplot(aes(x = totchol, y = cursmoke, group = sex, color = sex)) +
geom_jitter(height = 0.1, alpha = 0.1) +
geom_smooth(lwd = 1.5) +
theme_bw() ## Warning: Removed 409 rows containing non-finite values (stat_smooth).## Warning: Removed 409 rows containing missing values (geom_point).
ANS: no difference
data %>%
select(cursmoke, sex, totchol) %>%
mutate(cursmoke = factor(cursmoke),
smoke_sex = interaction(cursmoke, sex)) %>%
ggplot(aes(y = totchol, x = smoke_sex)) +
geom_boxplot(outlier.colour = "white") +
theme_bw() ## Warning: Removed 409 rows containing non-finite values (stat_boxplot).
Missingness
library(dplyr)
prop <- round(colSums(is.na(data))/dim(data)[1], 3)
knitr::kable(sort(prop, decreasing = TRUE)[1:9], col.names = "Proportion of NAs")| Proportion of NAs | |
|---|---|
| hdlc | 0.740 |
| ldlc | 0.740 |
| glucose | 0.124 |
| bpmeds | 0.051 |
| totchol | 0.035 |
| educ | 0.025 |
| cigpday | 0.007 |
| bmi | 0.004 |
| heartrte | 0.001 |
#MISSING DATA ANALYSIS
VIM::aggr(data, prop=T, numbers=T)## Warning in plot.aggr(res, ...): not enough vertical space to display
## frequencies (too many combinations)
mice::md.pattern(data)
## randid sex age sysbp diabp cursmoke diabetes prevchd prevap prevmi
## 2236 1 1 1 1 1 1 1 1 1 1
## 7074 1 1 1 1 1 1 1 1 1 1
## 267 1 1 1 1 1 1 1 1 1 1
## 1 1 1 1 1 1 1 1 1 1 1
## 683 1 1 1 1 1 1 1 1 1 1
## 267 1 1 1 1 1 1 1 1 1 1
## 132 1 1 1 1 1 1 1 1 1 1
## 157 1 1 1 1 1 1 1 1 1 1
## 9 1 1 1 1 1 1 1 1 1 1
## 121 1 1 1 1 1 1 1 1 1 1
## 252 1 1 1 1 1 1 1 1 1 1
## 3 1 1 1 1 1 1 1 1 1 1
## 6 1 1 1 1 1 1 1 1 1 1
## 70 1 1 1 1 1 1 1 1 1 1
## 180 1 1 1 1 1 1 1 1 1 1
## 1 1 1 1 1 1 1 1 1 1 1
## 16 1 1 1 1 1 1 1 1 1 1
## 3 1 1 1 1 1 1 1 1 1 1
## 3 1 1 1 1 1 1 1 1 1 1
## 6 1 1 1 1 1 1 1 1 1 1
## 9 1 1 1 1 1 1 1 1 1 1
## 3 1 1 1 1 1 1 1 1 1 1
## 47 1 1 1 1 1 1 1 1 1 1
## 9 1 1 1 1 1 1 1 1 1 1
## 1 1 1 1 1 1 1 1 1 1 1
## 9 1 1 1 1 1 1 1 1 1 1
## 1 1 1 1 1 1 1 1 1 1 1
## 2 1 1 1 1 1 1 1 1 1 1
## 4 1 1 1 1 1 1 1 1 1 1
## 1 1 1 1 1 1 1 1 1 1 1
## 7 1 1 1 1 1 1 1 1 1 1
## 23 1 1 1 1 1 1 1 1 1 1
## 2 1 1 1 1 1 1 1 1 1 1
## 7 1 1 1 1 1 1 1 1 1 1
## 1 1 1 1 1 1 1 1 1 1 1
## 2 1 1 1 1 1 1 1 1 1 1
## 4 1 1 1 1 1 1 1 1 1 1
## 1 1 1 1 1 1 1 1 1 1 1
## 1 1 1 1 1 1 1 1 1 1 1
## 1 1 1 1 1 1 1 1 1 1 1
## 1 1 1 1 1 1 1 1 1 1 1
## 1 1 1 1 1 1 1 1 1 1 1
## 1 1 1 1 1 1 1 1 1 1 1
## 2 1 1 1 1 1 1 1 1 1 1
## 0 0 0 0 0 0 0 0 0 0
## prevstrk prevhyp time period death angina hospmi mi_fchd anychd
## 2236 1 1 1 1 1 1 1 1 1
## 7074 1 1 1 1 1 1 1 1 1
## 267 1 1 1 1 1 1 1 1 1
## 1 1 1 1 1 1 1 1 1 1
## 683 1 1 1 1 1 1 1 1 1
## 267 1 1 1 1 1 1 1 1 1
## 132 1 1 1 1 1 1 1 1 1
## 157 1 1 1 1 1 1 1 1 1
## 9 1 1 1 1 1 1 1 1 1
## 121 1 1 1 1 1 1 1 1 1
## 252 1 1 1 1 1 1 1 1 1
## 3 1 1 1 1 1 1 1 1 1
## 6 1 1 1 1 1 1 1 1 1
## 70 1 1 1 1 1 1 1 1 1
## 180 1 1 1 1 1 1 1 1 1
## 1 1 1 1 1 1 1 1 1 1
## 16 1 1 1 1 1 1 1 1 1
## 3 1 1 1 1 1 1 1 1 1
## 3 1 1 1 1 1 1 1 1 1
## 6 1 1 1 1 1 1 1 1 1
## 9 1 1 1 1 1 1 1 1 1
## 3 1 1 1 1 1 1 1 1 1
## 47 1 1 1 1 1 1 1 1 1
## 9 1 1 1 1 1 1 1 1 1
## 1 1 1 1 1 1 1 1 1 1
## 9 1 1 1 1 1 1 1 1 1
## 1 1 1 1 1 1 1 1 1 1
## 2 1 1 1 1 1 1 1 1 1
## 4 1 1 1 1 1 1 1 1 1
## 1 1 1 1 1 1 1 1 1 1
## 7 1 1 1 1 1 1 1 1 1
## 23 1 1 1 1 1 1 1 1 1
## 2 1 1 1 1 1 1 1 1 1
## 7 1 1 1 1 1 1 1 1 1
## 1 1 1 1 1 1 1 1 1 1
## 2 1 1 1 1 1 1 1 1 1
## 4 1 1 1 1 1 1 1 1 1
## 1 1 1 1 1 1 1 1 1 1
## 1 1 1 1 1 1 1 1 1 1
## 1 1 1 1 1 1 1 1 1 1
## 1 1 1 1 1 1 1 1 1 1
## 1 1 1 1 1 1 1 1 1 1
## 1 1 1 1 1 1 1 1 1 1
## 2 1 1 1 1 1 1 1 1 1
## 0 0 0 0 0 0 0 0 0
## stroke cvd hyperten timeap timemi timemifc timechd timestrk timecvd
## 2236 1 1 1 1 1 1 1 1 1
## 7074 1 1 1 1 1 1 1 1 1
## 267 1 1 1 1 1 1 1 1 1
## 1 1 1 1 1 1 1 1 1 1
## 683 1 1 1 1 1 1 1 1 1
## 267 1 1 1 1 1 1 1 1 1
## 132 1 1 1 1 1 1 1 1 1
## 157 1 1 1 1 1 1 1 1 1
## 9 1 1 1 1 1 1 1 1 1
## 121 1 1 1 1 1 1 1 1 1
## 252 1 1 1 1 1 1 1 1 1
## 3 1 1 1 1 1 1 1 1 1
## 6 1 1 1 1 1 1 1 1 1
## 70 1 1 1 1 1 1 1 1 1
## 180 1 1 1 1 1 1 1 1 1
## 1 1 1 1 1 1 1 1 1 1
## 16 1 1 1 1 1 1 1 1 1
## 3 1 1 1 1 1 1 1 1 1
## 3 1 1 1 1 1 1 1 1 1
## 6 1 1 1 1 1 1 1 1 1
## 9 1 1 1 1 1 1 1 1 1
## 3 1 1 1 1 1 1 1 1 1
## 47 1 1 1 1 1 1 1 1 1
## 9 1 1 1 1 1 1 1 1 1
## 1 1 1 1 1 1 1 1 1 1
## 9 1 1 1 1 1 1 1 1 1
## 1 1 1 1 1 1 1 1 1 1
## 2 1 1 1 1 1 1 1 1 1
## 4 1 1 1 1 1 1 1 1 1
## 1 1 1 1 1 1 1 1 1 1
## 7 1 1 1 1 1 1 1 1 1
## 23 1 1 1 1 1 1 1 1 1
## 2 1 1 1 1 1 1 1 1 1
## 7 1 1 1 1 1 1 1 1 1
## 1 1 1 1 1 1 1 1 1 1
## 2 1 1 1 1 1 1 1 1 1
## 4 1 1 1 1 1 1 1 1 1
## 1 1 1 1 1 1 1 1 1 1
## 1 1 1 1 1 1 1 1 1 1
## 1 1 1 1 1 1 1 1 1 1
## 1 1 1 1 1 1 1 1 1 1
## 1 1 1 1 1 1 1 1 1 1
## 1 1 1 1 1 1 1 1 1 1
## 2 1 1 1 1 1 1 1 1 1
## 0 0 0 0 0 0 0 0 0
## timedth timehyp heartrte bmi cigpday educ totchol bpmeds glucose hdlc
## 2236 1 1 1 1 1 1 1 1 1 1
## 7074 1 1 1 1 1 1 1 1 1 0
## 267 1 1 1 1 1 1 1 1 0 1
## 1 1 1 1 1 1 1 1 1 0 1
## 683 1 1 1 1 1 1 1 1 0 0
## 267 1 1 1 1 1 1 1 0 1 1
## 132 1 1 1 1 1 1 1 0 1 0
## 157 1 1 1 1 1 1 1 0 0 1
## 9 1 1 1 1 1 1 1 0 0 0
## 121 1 1 1 1 1 1 0 1 1 0
## 252 1 1 1 1 1 1 0 1 0 0
## 3 1 1 1 1 1 1 0 0 1 0
## 6 1 1 1 1 1 1 0 0 0 0
## 70 1 1 1 1 1 0 1 1 1 1
## 180 1 1 1 1 1 0 1 1 1 0
## 1 1 1 1 1 1 0 1 1 0 1
## 16 1 1 1 1 1 0 1 1 0 0
## 3 1 1 1 1 1 0 1 0 1 1
## 3 1 1 1 1 1 0 1 0 1 0
## 6 1 1 1 1 1 0 0 1 1 0
## 9 1 1 1 1 1 0 0 1 0 0
## 3 1 1 1 1 0 1 1 1 1 1
## 47 1 1 1 1 0 1 1 1 1 0
## 9 1 1 1 1 0 1 1 1 0 0
## 1 1 1 1 1 0 1 1 0 1 0
## 9 1 1 1 1 0 1 1 0 0 1
## 1 1 1 1 1 0 1 0 1 1 0
## 2 1 1 1 1 0 1 0 1 0 0
## 4 1 1 1 1 0 0 1 1 1 0
## 1 1 1 1 1 0 0 0 1 0 0
## 7 1 1 1 0 1 1 1 1 1 1
## 23 1 1 1 0 1 1 1 1 1 0
## 2 1 1 1 0 1 1 1 1 0 1
## 7 1 1 1 0 1 1 1 1 0 0
## 1 1 1 1 0 1 1 1 0 1 1
## 2 1 1 1 0 1 1 0 1 1 0
## 4 1 1 1 0 1 1 0 1 0 0
## 1 1 1 1 0 1 0 1 1 1 1
## 1 1 1 1 0 1 0 1 1 1 0
## 1 1 1 0 1 1 1 1 1 1 0
## 1 1 1 0 1 1 1 0 1 0 0
## 1 1 1 0 0 1 1 1 1 0 0
## 1 1 1 0 0 1 1 0 1 0 0
## 2 1 1 0 0 0 1 1 0 0 1
## 0 0 6 52 79 295 409 593 1440 8600
## ldlc
## 2236 1 0
## 7074 0 2
## 267 1 1
## 1 0 2
## 683 0 3
## 267 1 1
## 132 0 3
## 157 1 2
## 9 0 4
## 121 0 3
## 252 0 4
## 3 0 4
## 6 0 5
## 70 1 1
## 180 0 3
## 1 1 2
## 16 0 4
## 3 1 2
## 3 0 4
## 6 0 4
## 9 0 5
## 3 1 1
## 47 0 3
## 9 0 4
## 1 0 4
## 9 1 3
## 1 0 4
## 2 0 5
## 4 0 4
## 1 0 6
## 7 1 1
## 23 0 3
## 2 1 2
## 7 0 4
## 1 1 2
## 2 0 4
## 4 0 5
## 1 1 2
## 1 0 4
## 1 0 3
## 1 0 5
## 1 0 5
## 1 0 6
## 2 1 5
## 8601 20075# HDLC and LDLC have a lot of missing data, and these variables should be eliminated
prob.data <- data %>%
group_by(period) %>%
summarise(sysbp_prob = sum(sysbp, na.rm = TRUE)/n())
prob.datatable(data$period)##
## 1 2 3
## 4434 3930 3263Models
library(lme4)
library(dplyr)- Is there a relationship between age and smoking status? Does this relationship differ by sex?
summary(gee::gee(cursmoke ~ age + sex + as.factor(educ) + bmi + diabetes+ heartrte + prevchd + prevstrk + prevhyp + timedth, id = randid, family=binomial, corstr = "unstructured"))## (Intercept) age sex as.factor(educ)2
## 6.0056791362 -0.0570318456 -0.7246241605 0.0503157656
## as.factor(educ)3 as.factor(educ)4 bmi diabetes
## -0.2263406725 -0.2104931713 -0.0940121564 -0.1114780579
## heartrte prevchd prevstrk prevhyp
## 0.0173911758 -0.0569530253 -0.2633153119 -0.2252617826
## timedth
## -0.0001021991##
## GEE: GENERALIZED LINEAR MODELS FOR DEPENDENT DATA
## gee S-function, version 4.13 modified 98/01/27 (1998)
##
## Model:
## Link: Logit
## Variance to Mean Relation: Binomial
## Correlation Structure: Unstructured
##
## Call:
## gee::gee(formula = cursmoke ~ age + sex + as.factor(educ) + bmi +
## diabetes + heartrte + prevchd + prevstrk + prevhyp + timedth,
## id = randid, family = binomial, corstr = "unstructured")
##
## Summary of Residuals:
## Min 1Q Median 3Q Max
## -0.8962482 -0.3999547 -0.2019900 0.4654084 0.9569903
##
##
## Coefficients:
## Estimate Naive S.E. Naive z Robust S.E.
## (Intercept) 5.865249e+00 2.876839e-01 20.3878246 2.918503e-01
## age -5.085698e-02 2.523157e-03 -20.1560927 2.409602e-03
## sex -7.161378e-01 5.853646e-02 -12.2340470 6.021884e-02
## as.factor(educ)2 8.329407e-02 6.878131e-02 1.2109985 7.132044e-02
## as.factor(educ)3 -1.824354e-01 8.341765e-02 -2.1870119 8.622144e-02
## as.factor(educ)4 -2.120259e-01 9.400901e-02 -2.2553781 9.703148e-02
## bmi -8.381699e-02 6.455452e-03 -12.9839063 6.897218e-03
## diabetes -6.038094e-02 9.758132e-02 -0.6187756 1.015290e-01
## heartrte 8.932497e-03 1.404441e-03 6.3601797 1.481180e-03
## prevchd -2.590671e-01 7.830011e-02 -3.3086429 9.019862e-02
## prevstrk -1.886466e-01 1.712697e-01 -1.1014592 1.758071e-01
## prevhyp -4.865095e-02 4.122989e-02 -1.1799922 4.099808e-02
## timedth -8.971112e-05 1.418953e-05 -6.3223476 1.414685e-05
## Robust z
## (Intercept) 20.0967721
## age -21.1059707
## sex -11.8922537
## as.factor(educ)2 1.1678849
## as.factor(educ)3 -2.1158935
## as.factor(educ)4 -2.1851244
## bmi -12.1522886
## diabetes -0.5947164
## heartrte 6.0306610
## prevchd -2.8721845
## prevstrk -1.0730321
## prevhyp -1.1866640
## timedth -6.3414186
##
## Estimated Scale Parameter: 0.9748127
## Number of Iterations: 4
##
## Working Correlation
## [,1] [,2] [,3]
## [1,] 1.0000000 0.7563191 0.5136670
## [2,] 0.7563191 1.0000000 0.5713635
## [3,] 0.5136670 0.5713635 1.0000000- Is there a relationship between the number of cigarettes smoked per day and age? Does this relationship differ by sex?
summary(gee::gee(cigpday ~ age + sex + as.factor(educ), id = randid, corstr = "unstructured")) ## (Intercept) age sex as.factor(educ)2
## 32.8474189 -0.2787825 -5.9230065 0.7894811
## as.factor(educ)3 as.factor(educ)4
## -0.7873846 -0.9535842##
## GEE: GENERALIZED LINEAR MODELS FOR DEPENDENT DATA
## gee S-function, version 4.13 modified 98/01/27 (1998)
##
## Model:
## Link: Identity
## Variance to Mean Relation: Gaussian
## Correlation Structure: Unstructured
##
## Call:
## gee::gee(formula = cigpday ~ age + sex + as.factor(educ), id = randid,
## corstr = "unstructured")
##
## Summary of Residuals:
## Min 1Q Median 3Q Max
## -16.938455 -7.957787 -4.031599 7.120862 77.643497
##
##
## Coefficients:
## Estimate Naive S.E. Naive z Robust S.E. Robust z
## (Intercept) 28.3465052 0.87303381 32.468966 0.88378195 32.074094
## age -0.1969624 0.01219203 -16.155019 0.01052473 -18.714256
## sex -6.0131712 0.31430105 -19.131884 0.33919691 -17.727671
## as.factor(educ)2 1.1048806 0.37423991 2.952332 0.39926096 2.767314
## as.factor(educ)3 -0.4829763 0.45051511 -1.072054 0.43622459 -1.107174
## as.factor(educ)4 -0.7195971 0.51224189 -1.404799 0.55221861 -1.303102
##
## Estimated Scale Parameter: 133.1198
## Number of Iterations: 3
##
## Working Correlation
## [,1] [,2] [,3]
## [1,] 1.0000000 0.7707103 0.4613932
## [2,] 0.7707103 1.0000000 0.5843157
## [3,] 0.4613932 0.5843157 1.0000000While answering these questions, please account for any confounders that you have evidence may impact the relationship between age and sex with smoking.
Next you are interested in the relationship between certain health outcomes and smoking status. In particular you are interested in:
- The relationship between current smoking status and systolic blood pressure.
summary(gee::gee(sysbp ~ cursmoke + age + sex + as.factor(educ), id = randid, na.action = "na.omit", corstr = "unstructured"))## (Intercept) cursmoke age sex
## 87.8024330 -2.0414490 0.8846592 1.2687106
## as.factor(educ)2 as.factor(educ)3 as.factor(educ)4
## -0.3063701 -2.9072926 -4.0416336##
## GEE: GENERALIZED LINEAR MODELS FOR DEPENDENT DATA
## gee S-function, version 4.13 modified 98/01/27 (1998)
##
## Model:
## Link: Identity
## Variance to Mean Relation: Gaussian
## Correlation Structure: Unstructured
##
## Call:
## gee::gee(formula = sysbp ~ cursmoke + age + sex + as.factor(educ),
## id = randid, na.action = "na.omit", corstr = "unstructured")
##
## Summary of Residuals:
## Min 1Q Median 3Q Max
## -56.456788 -14.552902 -2.892551 11.072266 147.850985
##
##
## Coefficients:
## Estimate Naive S.E. Naive z Robust S.E. Robust z
## (Intercept) 88.9127308 1.71558828 51.826380 1.65360529 53.769017
## cursmoke -1.5149317 0.46476110 -3.259592 0.45715635 -3.313815
## age 0.8653711 0.02377869 36.392712 0.02294929 37.707974
## sex 1.4262673 0.54709991 2.606959 0.57967657 2.460454
## as.factor(educ)2 -0.7481716 0.64772860 -1.155070 0.69947330 -1.069621
## as.factor(educ)3 -3.1296696 0.77855475 -4.019845 0.82616759 -3.788178
## as.factor(educ)4 -4.3249661 0.88481499 -4.887989 0.91529976 -4.725191
##
## Estimated Scale Parameter: 438.277
## Number of Iterations: 3
##
## Working Correlation
## [,1] [,2] [,3]
## [1,] 1.0000000 0.5844383 0.3901881
## [2,] 0.5844383 1.0000000 0.4769521
## [3,] 0.3901881 0.4769521 1.0000000- The relationship between current smoking status and diastolic blood pressure.
summary(gee::gee(diabp ~ cursmoke + age + sex + as.factor(educ), id = randid, na.action = "na.omit", corstr = "unstructured"))## (Intercept) cursmoke age sex
## 83.14931183 -1.76253559 0.06074128 -1.49015111
## as.factor(educ)2 as.factor(educ)3 as.factor(educ)4
## -0.07960126 -0.96361582 -1.38809040##
## GEE: GENERALIZED LINEAR MODELS FOR DEPENDENT DATA
## gee S-function, version 4.13 modified 98/01/27 (1998)
##
## Model:
## Link: Identity
## Variance to Mean Relation: Gaussian
## Correlation Structure: Unstructured
##
## Call:
## gee::gee(formula = diabp ~ cursmoke + age + sex + as.factor(educ),
## id = randid, na.action = "na.omit", corstr = "unstructured")
##
## Summary of Residuals:
## Min 1Q Median 3Q Max
## -53.815474 -7.934818 -1.165221 6.612862 66.053172
##
##
## Coefficients:
## Estimate Naive S.E. Naive z Robust S.E. Robust z
## (Intercept) 83.72716018 0.94598765 88.5076670 0.92664562 90.3551025
## cursmoke -1.25577390 0.25866115 -4.8548996 0.26295278 -4.7756631
## age 0.04492311 0.01318527 3.4070687 0.01301711 3.4510820
## sex -1.37262875 0.29612384 -4.6353199 0.31463807 -4.3625640
## as.factor(educ)2 -0.20708873 0.35071588 -0.5904743 0.38142348 -0.5429365
## as.factor(educ)3 -1.00717792 0.42133624 -2.3904374 0.43642586 -2.3077870
## as.factor(educ)4 -1.50398297 0.47863392 -3.1422407 0.49916228 -3.0130140
##
## Estimated Scale Parameter: 134.5107
## Number of Iterations: 3
##
## Working Correlation
## [,1] [,2] [,3]
## [1,] 1.0000000 0.5561530 0.3490568
## [2,] 0.5561530 1.0000000 0.3838573
## [3,] 0.3490568 0.3838573 1.0000000- The relationship between current smoking status and serum total cholesterol.
summary(gee::gee(totchol ~ cursmoke + age + sex + as.factor(educ), id = randid, na.action = "na.omit", corstr = "unstructured"))## (Intercept) cursmoke age sex
## 180.5972060 1.6590353 0.7348726 12.0862772
## as.factor(educ)2 as.factor(educ)3 as.factor(educ)4
## 0.9107182 2.0078913 0.6363909##
## GEE: GENERALIZED LINEAR MODELS FOR DEPENDENT DATA
## gee S-function, version 4.13 modified 98/01/27 (1998)
##
## Model:
## Link: Identity
## Variance to Mean Relation: Gaussian
## Correlation Structure: Unstructured
##
## Call:
## gee::gee(formula = totchol ~ cursmoke + age + sex + as.factor(educ),
## id = randid, na.action = "na.omit", corstr = "unstructured")
##
## Summary of Residuals:
## Min 1Q Median 3Q Max
## -148.090340 -29.650053 -2.060511 27.146185 399.388552
##
##
## Coefficients:
## Estimate Naive S.E. Naive z Robust S.E. Robust z
## (Intercept) 179.4752160 3.62072716 49.5688319 3.65765697 49.0683565
## cursmoke 2.2459560 0.97321653 2.3077660 0.99901818 2.2481633
## age 0.7164736 0.04953822 14.4630466 0.04903112 14.6126292
## sex 12.7309870 1.18566784 10.7373976 1.22285054 10.4109101
## as.factor(educ)2 1.0663777 1.40446547 0.7592766 1.49560440 0.7130079
## as.factor(educ)3 2.1301734 1.68938577 1.2609159 1.78623276 1.1925509
## as.factor(educ)4 0.9692929 1.91708122 0.5056087 1.85486438 0.5225681
##
## Estimated Scale Parameter: 1956.654
## Number of Iterations: 3
##
## Working Correlation
## [,1] [,2] [,3]
## [1,] 1.0000000 0.6715907 0.4279521
## [2,] 0.6715907 1.0000000 0.4618901
## [3,] 0.4279521 0.4618901 1.0000000model_1<-glmer(cursmoke~ age + sex + sysbp + diabp + totchol + as.factor(educ) + (1|randid), family=binomial, na.action = "na.omit")## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl =
## control$checkConv, : Model failed to converge with max|grad| = 1.19128 (tol
## = 0.001, component 1)## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: very large eigenvalue
## - Rescale variables?;Model is nearly unidentifiable: large eigenvalue ratio
## - Rescale variables?knitr::kable(summary(model_1)$coefficients,digits = 3)| Estimate | Std. Error | z value | Pr(>|z|) | |
|---|---|---|---|---|
| (Intercept) | 16.730 | 0.965 | 17.332 | 0.000 |
| age | -0.206 | 0.010 | -20.134 | 0.000 |
| sex | -3.760 | 0.324 | -11.597 | 0.000 |
| sysbp | -0.001 | 0.005 | -0.193 | 0.847 |
| diabp | -0.027 | 0.008 | -3.341 | 0.001 |
| totchol | 0.005 | 0.002 | 3.029 | 0.002 |
| as.factor(educ)2 | 0.922 | 0.284 | 3.245 | 0.001 |
| as.factor(educ)3 | -0.330 | 0.326 | -1.014 | 0.311 |
| as.factor(educ)4 | -0.481 | 0.372 | -1.293 | 0.196 |
glmer(cursmoke~ age + sex + totchol + as.factor(educ) + bmi + diabetes+ heartrte + prevchd + prevstrk + prevhyp + timedth + (1|randid), family=binomial, na.action = "na.omit") %>% knitr::kable(summary(.)$coefficients,digits = 3) # too many covariates to convergeREPORT
What to Turn In: For this assignment you will turn in a single pdf document with (a) your summary of findings and (b) an Appendix with figures and (c) an Appendix with all R code (in the form of a knited pdf).
OBJECTIVE:
An objective or description of the goals of the analysis
We are interested to describe the smoking habits of the participants in the Framingham Heart study as they age and the impact of smoking on certain health outcomes. The Framingham heart study asks participants about their smoking habits at each visit. In particular, participants are asked if they are currently smoking at this visit (0 = Not a current smoker, 1 = Current smoker), which we will refer to as current smoking status. In addition, participants also report the number of cigarettes they are smoking per day. A more complete description of each of variables in the Framingham Heart study can be found in the Framingham Heart Study Longitudinal Data Documentation.
We are interested to answer the following questions:
Is there a relationship between age and smoking status? Does this relationship differ by sex?
Is there a relationship between the number of cigarettes smoked per day and age? Does this relationship differ by sex?
The relationship between current smoking status and systolic blood pressure.
The relationship between current smoking status and diastolic blood pressure.
The relationship between current smoking status and serum total cholesterol.
STUDY DESIGN:
A brief description of the study design and the data
METHODS:
A methods section describing your statistical analysis (please justify all modeling choices that were made with evidence).
TO INCLUDE:
age - we want to see how smoking status changes as we get older
sex - exploratory data analysis showed there were differences
education - found in the literature
total cholesterol
BMI - confounder based on literature
diabetes (https://www.cdc.gov/tobacco/data_statistics/sgr/50th-anniversary/pdfs/fs_smoking_diabetes_508.pdf)
heart rate - smoking increases heart rate (in literature)
prevchd since prevmi and prevap are correlaed
prevstroke
prevhyp
timedth
DONT INCLUDE: systolic, diastolic bc we have hypertension
BPmeds - not significant
LDL and HDL have too many NAs
glucose - correlated with diabetes
RESULTS:
A results section that includes a) descriptive statistics for the data b) a summary of your key findings including supporting numerical summaries (i.e. confidence intervals, pvalues, etc.) c) interpretations of your key findings (i.e. interpretations of coefficients).
CONCLUSION:
A conclusion specifically answering the objective of the analysis.